Higher-order Carmichael numbers
| dc.creator | Howe, Everett W. | |
| dc.date | 1998-12-16 | |
| dc.date.accessioned | 2026-07-07T05:27:15Z | |
| dc.date.available | 2026-07-07T05:27:15Z | |
| dc.description | We define a Carmichael number of order m to be a composite integer n such that nth-power raising defines an endomorphism of every Z/nZ-algebra that can be generated as a Z/nZ-module by m elements. We give a simple criterion to determine whether a number is a Carmichael number of order m, and we give a heuristic argument (based on an argument of Erdos for the usual Carmichael numbers) that indicates that for every m there should be infinitely many Carmichael numbers of order m. The argument suggests a method for finding examples of higher-order Carmichael numbers; we use the method to provide examples of Carmichael numbers of order 2. | |
| dc.description | 9 pages, AMS-LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/9812089 | |
| dc.identifier | http://arxiv.org/abs/math/9812089 | |
| dc.identifier | Math. Comp. 69 (2000) 1711--1719. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77849 | |
| dc.subject | Number Theory | |
| dc.subject | Commutative Algebra | |
| dc.subject | 11A51 (Primary) 11N25, 11Y11, 13B40 (Secondary) | |
| dc.title | Higher-order Carmichael numbers | |
| dc.type | text |